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[1] Gu Jianxin, Chan Siulai,. New tangent stiffness matrixfor geometrically nonlinear analysis of space frames [J]. Journal of Southeast University (English Edition), 2005, 21 (4): 480-485. [doi:10.3969/j.issn.1003-7985.2005.04.021]
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New tangent stiffness matrixfor geometrically nonlinear analysis of space frames()
一种用于空间框架结构几何非线性分析的切线刚度矩阵
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
21
Issue:
2005 4
Page:
480-485
Research Field:
Civil Engineering
Publishing date:
2005-12-30

Info

Title:
New tangent stiffness matrixfor geometrically nonlinear analysis of space frames
一种用于空间框架结构几何非线性分析的切线刚度矩阵
Author(s):
Gu Jianxin1;  Chan Siulai2
1 Library, Southeast University, Nanjing 210096, China
2Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hong Kong, China
顾建新1;  陈绍礼2
1东南大学图书馆, 南京210096; 2香港理工大学土木与结构工程系, 中国香港
Keywords:
beam elements;  space frames;  tangent stiffness matrix;  flexural-torsional buckling;  second-order effects;  geometric nonlinearity
梁单元;  空间框架;  切线刚度矩阵;  弯扭屈曲;  二阶效应;  几何非线性
PACS:
TU323.5
DOI:
10.3969/j.issn.1003-7985.2005.04.021
Abstract:
A three-dimensional beam element is derived based on the principle of stationary total potential energy for geometrically nonlinear analysis of space frames.A new tangent stiffness matrix, which allows for high order effects of element deformations, replaces the conventional incremental secant stiffness matrix.Two deformation stiffness matrices due to the variation of axial force and bending moments are included in the tangent stiffness.They are functions of element deformations and incorporate the coupling among axial, lateral and torsional deformations.A correction matrix is added to the tangent stiffness matrix to make displacement derivatives equivalent to the commutative rotational degrees of freedom.Numerical examples show that the proposed element is accurate and efficient in predicting the nonlinear behavior, such as axial-torsional and flexural-torsional buckling, of space frames even when fewer elements are used to model a member.
为了改善空间框架结构的几何非线性分析, 根据总势能驻值原理推导了一个三维梁单元, 用增量切线刚度矩阵代替传统的增量割线刚度矩阵.新的切线刚度矩阵除了常用的线性刚度和几何刚度矩阵外, 还包含2个变形刚度矩阵, 这2个矩阵是由每个增量步中轴力和弯距的变化引起的, 是单元变形的函数, 包含轴向、横向和扭转变形的耦合项.考虑空间转动和弯距的特征, 增加一个修正矩阵, 使提出的单元通过刚体测试, 达到良好的收敛性能.实例显示使用较少的单元模拟构件仍可有效、准确地得到空间框架的轴向扭转和弯扭屈曲的非线性性能.

References:

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Memo

Memo:
Biographies: Gu Jianxin(1961—), male, doctor, associate professor, gujx@seu.edu.cn;Chan Siulai(1957—), male, doctor, professor, ceslchan@polyu.edu.hk.
Last Update: 2005-12-20